Summary Similar to graphite and graphene, aromatic rings are ultra-stable configurations with highly delocalized sp2-hybridized electrons, which are the basic units for most organic electrode materials. However, the aromatic rings in organic electrode materials are inaccessible for Na+-ion storage. Here, we have designed a wavy-layered 3D structure of metal-organic compound zinc perylenetetracarboxylates (Zn-PTCA) with stretched space between adjacent perylene planes, which enables aromatic rings activated as Na+-ion storage sites. Such Zn-PTCA delivers a high specific capacity of 357 mAh g−1 at a current density of 50 mA g−1 within the potential range of 0.01–2 V versus Na+/Na, corresponding to an eight-electron-transfer process. Experiments and calculations revealed that both C=O groups and aromatic rings are involved in the Na insertion processes. We believe that the present strategy can open up an avenue for developing a big family of 3D open-framework-structured organic materials for application in high-capacity Na+-ion batteries.